CatDat

initial-object-preserving

A functor $F$ preserves initial objects when it maps every initial object to an initial object. It is not assumed that the source category has a initial object.

• Dual property: terminal-object-preserving

Relevant implications

• finite-coproduct-preserving implies initial-object-preserving
• right exact implies finite-coproduct-preserving andinitial-object-preserving

*Those implications also require assumptions on the source or target category.

Examples

There are 3 functors with this property.

• abelianization functor for groups
• free group functor
• identity functor on the category of sets

Counterexamples

There are 3 functors without this property.

• contravariant power set functor
• covariant power set functor
• forgetful functor for vector spaces

Unknown

There are 0 functors for which the database has no information on whether they satisfy this property.

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